VTOL Hover Balance: Thrust Vectoring

Engine Controls

Throttle (main nozzle) 100%

Nozzle vector angle δ 0°

Roll trim (puffer jets) 0%

Trim throttle to hold altitude

Flight State

Altitude

15.0 m

Vertical speed

0.00 m/s

Pitch angle

0.0°

Roll angle

0.0°

Thrust / Weight

1.00

Pitch rate

0.0°/s

How it works

A jump-jet VTOL (Harrier, F-35B in hover mode) has no wings doing useful work at zero airspeed, so every newton of lift and every control moment comes from vectored engine thrust. The main nozzle can swivel through an angle δ, splitting its thrust F into a vertical and horizontal component:

F_vertical = F · cos(δ)
F_horizontal = F · sin(δ)
Pitch torque τ_p = F · sin(δ) · d_arm − c_p · ω_p   (d_arm = nozzle offset from CG)

Roll has no aerodynamic control surfaces to use either, so real jump-jets bleed compressed bypass air to small "puffer" reaction-control jets in the wingtips. Firing them unevenly produces a pure roll torque with no vertical-thrust penalty:

τ_roll = k_roll · trim − c_r · ω_r
θ(t+dt) = θ(t) + ω(t)·dt,   ω(t+dt) = ω(t) + (τ/I)·dt

The aircraft is a rigid body: Throttle sets main thrust magnitude F (100% ≈ hover thrust, matching weight); Nozzle vector angle tilts F to control pitch and horizontal drift; Roll trim commands the puffer jets directly. Gust injects a random disturbance torque each second, the way real crosswind gusts upset a hovering jump-jet, so you must actively counter it — exactly the closed-loop balancing problem a VTOL flight-control computer solves automatically in real aircraft.

Main nozzle exhaust Puffer (roll) jets

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